Abstract

BRACAMONTE, Mireya; GIMENEZ, José  and  MEDINA, Jesús. Sandwich theorem for reciprocally strongly convex functions. Rev.colomb.mat. [online]. 2018, vol.52, n.2, pp.171-184. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v52n2.77157.

We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy

for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h: [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b].

Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

Keywords : Convex functions; Sandwich theorem; Hyers-Ulam.

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